Subgroups — C₂×C₇×#3537 #13239940

Order 1792.

8890 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3537	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₇×#553	C₂	1	4	yes	maximal, complemented
4	C₂×C₇×D₄²	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×D₄²	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#540	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#534	C₂	1	4	yes	maximal, complemented
10	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×#121	C₂	1	2	yes	maximal, complemented
12	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
14	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
15	C₂³×C₇×D₄	C₂²	1	8	yes	complemented
16	C₂³×C₇×D₄	C₂²	1	2	yes	complemented
17	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
18	C₇×#560	C₂²	1	64	yes	complemented
19	C₇×#553	C₂²	1	64	yes	complemented
20	C₇×D₄²	C₂²	1	64	yes	complemented
21	C₇×D₄²	C₂²	1	64	yes	complemented
22	C₇×#540	C₂²	1	32	yes	complemented
23	C₇×#538	C₂²	1	64	yes	complemented
24	C₇×#535	C₂²	1	32	yes	complemented
25	C₇×#534	C₂²	1	64	yes	complemented
26	C₂×C₇×#127	C₂²	1	4	yes	complemented
27	C₂×C₇×#127	C₂²	1	2	yes	complemented
28	C₂×C₇×#126	C₂²	1	8	yes	complemented
29	C₂×C₇×#125	C₂²	1	2	yes	complemented
30	C₂×C₇×#124	C₂²	1	4	yes	complemented
31	C₇×#525	C₂²	1	16	yes	complemented
32	C₂×C₇×#123	C₂²	1	2	yes	complemented
33	C₂×C₇×#123	C₂²	1	8	yes	complemented
34	C₂×C₇×#123	C₂²	1	8	yes	complemented
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₇×#121	C₂²	1	4	yes	complemented
37	C₂×C₇×#121	C₂²	1	4	yes	complemented
38	C₂×C₇×#121	C₂²	1	4	yes	complemented
39	C₂×C₇×#121	C₂²	1	4	yes	complemented
40	C₂×C₇×#121	C₂²	1	2	yes	complemented
41	C₂×C₇×#121	C₂²	1	8	yes	complemented
42	C₂×C₇×#121	C₂²	1	4	yes	complemented
43	C₂×C₇×#121	C₂²	1	8	yes	complemented
44	C₂×C₇×#121	C₂²	1	8	yes	complemented
45	C₂×C₇×#121	C₂²	1	32	yes	complemented
46	C₂×C₇×#120	C₂²	1	2	yes	complemented
47	C₂×C₇×#120	C₂²	1	4	yes	complemented
48	C₂×C₇×#120	C₂²	1	8	yes	complemented
49	C₂×C₇×#120	C₂²	1	4	yes	complemented
50	C₂×C₇×#120	C₂²	1	8	yes	complemented
51	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
52	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
53	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
54	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₇×#117	C₂²	1	2	yes	complemented
56	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
57	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
58	C₂×#3537	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁵×C₇	C₂³	1	1	yes	characteristic
60	C₂⁵×C₇	C₂³	1	4	yes	—
61	C₂⁵×C₇	C₂³	1	4	yes	—
62	C₂×C₇×#41	—	4	4	no	—
63	C₂×C₇×#41	C₂³	1	8	yes	complemented
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	4	8	no	—
66	C₂²×C₇×D₄	—	4	8	no	—
67	C₂²×C₇×D₄	—	4	16	no	—
68	C₂²×C₇×D₄	—	4	32	no	—
69	C₂²×C₇×D₄	C₂³	1	8	yes	—
70	C₂²×C₇×D₄	C₂³	1	4	yes	—
71	C₂²×C₇×D₄	C₂³	1	4	yes	—
72	C₂²×C₇×D₄	C₂³	1	4	yes	—
73	C₂²×C₇×D₄	C₂³	1	8	yes	—
74	C₂²×C₇×D₄	C₂³	1	8	yes	—
75	C₂²×C₇×D₄	C₂³	1	4	yes	—
76	C₂²×C₇×D₄	C₂³	1	8	yes	—
77	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
78	C₂²×C₇×D₄	C₂³	1	2	yes	—
79	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
80	C₂²×C₇×D₄	C₂³	1	32	yes	complemented
81	C₂²×C₇×D₄	C₂³	1	64	yes	complemented
82	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
83	C₂³×C₄×C₇	—	4	4	no	—
84	C₂³×C₄×C₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₇	C₂³	1	8	yes	—
89	C₂³×C₄×C₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	8	yes	complemented
92	C₇×#127	C₂³	1	32	yes	complemented
93	C₇×#127	C₂³	1	16	yes	complemented
94	C₇×#126	C₂³	1	64	yes	complemented
95	C₇×#125	C₂³	1	16	yes	complemented
96	C₇×#124	C₂³	1	32	yes	complemented
97	C₇×#123	C₂³	1	16	yes	complemented
98	C₇×#123	C₂³	1	64	yes	complemented
99	C₇×#123	C₂³	1	64	yes	complemented
100	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
101	C₇×#121	C₂³	1	32	yes	complemented
102	C₇×#121	C₂³	1	32	yes	complemented
103	C₇×#121	C₂³	1	32	yes	complemented
104	C₇×#121	C₂³	1	32	yes	complemented
105	C₇×#121	C₂³	1	16	yes	complemented
106	C₇×#121	C₂³	1	64	yes	complemented
107	C₇×#121	C₂³	1	32	yes	complemented
108	C₇×#121	C₂³	1	64	yes	complemented
109	C₇×#121	C₂³	1	64	yes	complemented
110	C₇×#120	C₂³	1	16	yes	complemented
111	C₇×#120	C₂³	1	32	yes	complemented
112	C₇×#120	C₂³	1	64	yes	complemented
113	C₇×#120	C₂³	1	32	yes	complemented
114	C₇×#120	C₂³	1	64	yes	complemented
115	C₄×C₇×D₄	C₂³	1	32	yes	complemented
116	C₄×C₇×D₄	C₂³	1	64	yes	complemented
117	C₄×C₇×D₄	C₂³	1	32	yes	complemented
118	C₇×#117	C₂³	1	8	yes	complemented
119	C₇×#117	C₂³	1	16	yes	complemented
120	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
125	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
126	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	complemented
135	C₂×C₄²×C₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₇	C₂³	1	4	yes	—
137	#3537	C₂×C₇	1	32	yes	direct product factor
138	C₂×#560	C₂×C₇	1	4	yes	complemented
139	C₂×#553	C₂×C₇	1	4	yes	complemented
140	C₂×D₄²	C₂×C₇	1	4	yes	complemented
141	C₂×D₄²	C₂×C₇	1	4	yes	complemented
142	C₂×#540	C₂×C₇	1	2	yes	complemented
143	C₂×#538	C₂×C₇	1	4	yes	complemented
144	C₂×#535	C₂×C₇	1	2	yes	complemented
145	C₂×#534	C₂×C₇	1	4	yes	complemented
146	C₂×#525	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂²×#121	C₂×C₇	1	2	yes	complemented
148	C₂⁴×C₇	—	2	8	no	—
149	C₂⁴×C₇	—	2	16	no	—
150	C₂⁴×C₇	—	4	2	no	—
151	C₂⁴×C₇	—	4	8	no	—
152	C₂⁴×C₇	—	4	8	no	—
153	C₂⁴×C₇	—	4	8	no	—
154	C₂⁴×C₇	—	4	16	no	—
155	C₂⁴×C₇	C₂⁴	1	2	yes	—
156	C₂⁴×C₇	C₂⁴	1	8	yes	—
157	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
158	C₂⁴×C₇	C₂⁴	1	4	yes	—
159	C₂⁴×C₇	C₂⁴	1	2	yes	—
160	C₂⁴×C₇	C₂⁴	1	16	yes	—
161	C₂⁴×C₇	C₂⁴	1	16	yes	—
162	C₇×#41	—	4	16	no	—
163	C₂×C₇×Q₈	—	4	2	no	—
164	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
165	C₂×C₇×D₄	—	2	32	no	—
166	C₂×C₇×D₄	—	2	16	no	—
167	C₂×C₇×D₄	—	2	16	no	—
168	C₂×C₇×D₄	—	4	32	no	—
169	C₂×C₇×D₄	—	4	32	no	—
170	C₂×C₇×D₄	—	4	8	no	—
171	C₂×C₇×D₄	—	4	8	no	—
172	C₂×C₇×D₄	—	4	16	no	—
173	C₂×C₇×D₄	—	4	16	no	—
174	C₂×C₇×D₄	—	4	16	no	—
175	C₂×C₇×D₄	—	4	2	no	—
176	C₂×C₇×D₄	—	4	4	no	—
177	C₂×C₇×D₄	—	4	64	no	—
178	C₂×C₇×D₄	—	4	128	no	—
179	C₂×C₇×D₄	C₂⁴	1	16	yes	—
180	C₂×C₇×D₄	C₂⁴	1	32	yes	—
181	C₂×C₇×D₄	C₂⁴	1	16	yes	—
182	C₂×C₇×D₄	C₂⁴	1	4	yes	—
183	C₂×C₇×D₄	C₂⁴	1	8	yes	—
184	C₂×C₇×D₄	C₂⁴	1	16	yes	—
185	C₂×C₇×D₄	C₂⁴	1	32	yes	—
186	C₂×C₇×D₄	C₂⁴	1	32	yes	—
187	C₂×C₇×D₄	C₂⁴	1	16	yes	—
188	C₂×C₇×D₄	C₂⁴	1	32	yes	—
189	C₂²×C₄×C₇	—	2	8	no	—
190	C₂²×C₄×C₇	—	2	4	no	—
191	C₂²×C₄×C₇	—	2	8	no	—
192	C₂²×C₄×C₇	—	4	16	no	—
193	C₂²×C₄×C₇	—	4	2	no	—
194	C₂²×C₄×C₇	—	4	4	no	—
195	C₂²×C₄×C₇	—	4	8	no	—
196	C₂²×C₄×C₇	—	4	16	no	—
197	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
203	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
206	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
207	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
208	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
210	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
211	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
212	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
213	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
214	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
215	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
216	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
217	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
218	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
219	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
220	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
221	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
222	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
223	C₄²×C₇	C₂⁴	1	8	yes	—
224	C₄²×C₇	C₂⁴	1	16	yes	—
225	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
226	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
227	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
228	C₂³×D₄	C₂²×C₇	1	8	yes	complemented
229	C₂³×D₄	C₂²×C₇	1	2	yes	complemented
230	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic, complemented
231	#560	C₂²×C₇	1	64	yes	complemented
232	#553	C₂²×C₇	1	64	yes	complemented
233	D₄²	C₂²×C₇	1	64	yes	complemented
234	D₄²	C₂²×C₇	1	64	yes	complemented
235	#540	C₂²×C₇	1	32	yes	complemented
236	#538	C₂²×C₇	1	64	yes	complemented
237	#535	C₂²×C₇	1	32	yes	complemented
238	#534	C₂²×C₇	1	64	yes	complemented
239	C₂×#127	C₂²×C₇	1	4	yes	complemented
240	C₂×#127	C₂²×C₇	1	2	yes	complemented
241	C₂×#126	C₂²×C₇	1	8	yes	complemented
242	C₂×#125	C₂²×C₇	1	2	yes	complemented
243	C₂×#124	C₂²×C₇	1	4	yes	complemented
244	#525	C₂²×C₇	1	16	yes	complemented
245	C₂×#123	C₂²×C₇	1	2	yes	complemented
246	C₂×#123	C₂²×C₇	1	8	yes	complemented
247	C₂×#123	C₂²×C₇	1	8	yes	complemented
248	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
249	C₂×#121	C₂²×C₇	1	4	yes	complemented
250	C₂×#121	C₂²×C₇	1	4	yes	complemented
251	C₂×#121	C₂²×C₇	1	4	yes	complemented
252	C₂×#121	C₂²×C₇	1	4	yes	complemented
253	C₂×#121	C₂²×C₇	1	2	yes	complemented
254	C₂×#121	C₂²×C₇	1	8	yes	complemented
255	C₂×#121	C₂²×C₇	1	4	yes	complemented
256	C₂×#121	C₂²×C₇	1	8	yes	complemented
257	C₂×#121	C₂²×C₇	1	8	yes	complemented
258	C₂×#121	C₂²×C₇	1	32	yes	complemented
259	C₂×#120	C₂²×C₇	1	2	yes	complemented
260	C₂×#120	C₂²×C₇	1	4	yes	complemented
261	C₂×#120	C₂²×C₇	1	8	yes	complemented
262	C₂×#120	C₂²×C₇	1	4	yes	complemented
263	C₂×#120	C₂²×C₇	1	8	yes	complemented
264	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
265	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
266	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
267	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
268	C₂×#117	C₂²×C₇	1	2	yes	complemented
269	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
270	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
271	C₂³×C₇	—	2	4	no	—
272	C₂³×C₇	—	2	4	no	—
273	C₂³×C₇	—	2	2	no	—
274	C₂³×C₇	—	2	4	no	—
275	C₂³×C₇	—	2	16	no	—
276	C₂³×C₇	—	2	8	no	—
277	C₂³×C₇	—	2	16	no	—
278	C₂³×C₇	—	2	16	no	—
279	C₂³×C₇	—	2	16	no	—
280	C₂³×C₇	—	2	4	no	—
281	C₂³×C₇	—	2	32	no	—
282	C₂³×C₇	—	4	4	no	—
283	C₂³×C₇	—	4	16	no	—
284	C₂³×C₇	—	4	16	no	—
285	C₂³×C₇	—	4	16	no	—
286	C₂³×C₇	—	4	32	no	—
287	C₂³×C₇	—	4	16	no	—
288	C₂³×C₇	—	8	32	no	—
289	C₂³×C₇	—	8	32	no	—
290	C₂³×C₇	H(5,𝔽₂)	1	8	yes	—
291	C₂³×C₇	C₂⁵	1	4	yes	—
292	C₂³×C₇	C₂⁵	1	16	yes	—
293	C₂³×C₇	C₂⁵	1	2	yes	—
294	C₂³×C₇	C₂⁵	1	4	yes	—
295	C₂³×C₇	C₂⁵	1	1	yes	characteristic
296	C₇×Q₈	—	4	4	no	—
297	C₇×D₄	—	2	64	no	—
298	C₇×D₄	—	2	32	no	—
299	C₇×D₄	—	2	32	no	—
300	C₇×D₄	—	4	16	no	—
301	C₇×D₄	—	4	16	no	—
302	C₇×D₄	—	4	32	no	—
303	C₇×D₄	—	4	32	no	—
304	C₇×D₄	—	4	32	no	—
305	C₇×D₄	—	4	4	no	—
306	C₇×D₄	—	4	8	no	—
307	C₂×C₄×C₇	—	2	4	no	—
308	C₂×C₄×C₇	—	2	2	no	—
309	C₂×C₄×C₇	—	2	4	no	—
310	C₂×C₄×C₇	—	2	16	no	—
311	C₂×C₄×C₇	—	2	8	no	—
312	C₂×C₄×C₇	—	2	16	no	—
313	C₂×C₄×C₇	—	2	8	no	—
314	C₂×C₄×C₇	—	2	16	no	—
315	C₂×C₄×C₇	—	4	4	no	—
316	C₂×C₄×C₇	—	4	8	no	—
317	C₂×C₄×C₇	—	4	16	no	—
318	C₂×C₄×C₇	—	4	32	no	—
319	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
320	C₂×C₄×C₇	C₂⁵	1	4	yes	—
321	C₂×C₄×C₇	C₂⁵	1	8	yes	—
322	C₂×C₄×C₇	C₂⁵	1	16	yes	—
323	C₂×C₄×C₇	C₂⁵	1	2	yes	—
324	C₂×C₄×C₇	C₂⁵	1	4	yes	—
325	C₂×C₄×C₇	C₂⁵	1	2	yes	—
326	C₂⁵	C₂³×C₇	1	1	yes	characteristic
327	C₂⁵	C₂³×C₇	1	4	yes	—
328	C₂⁵	C₂³×C₇	1	4	yes	—
329	C₂×#41	—	4	4	no	—
330	C₂×#41	C₂³×C₇	1	8	yes	complemented
331	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×D₄	—	4	8	no	—
333	C₂²×D₄	—	4	8	no	—
334	C₂²×D₄	—	4	16	no	—
335	C₂²×D₄	—	4	32	no	—
336	C₂²×D₄	C₂³×C₇	1	4	yes	—
337	C₂²×D₄	C₂³×C₇	1	8	yes	—
338	C₂²×D₄	C₂³×C₇	1	4	yes	—
339	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
340	C₂²×D₄	C₂³×C₇	1	2	yes	—
341	C₂²×D₄	C₂³×C₇	1	4	yes	—
342	C₂²×D₄	C₂³×C₇	1	8	yes	—
343	C₂²×D₄	C₂³×C₇	1	8	yes	—
344	C₂²×D₄	C₂³×C₇	1	4	yes	—
345	C₂²×D₄	C₂³×C₇	1	8	yes	—
346	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
347	C₂²×D₄	C₂³×C₇	1	32	yes	complemented
348	C₂²×D₄	C₂³×C₇	1	64	yes	complemented
349	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
350	C₂³×C₄	—	4	4	no	—
351	C₂³×C₄	C₂³×C₇	1	2	yes	—
352	C₂³×C₄	C₂³×C₇	1	2	yes	—
353	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₇	1	2	yes	—
355	C₂³×C₄	C₂³×C₇	1	4	yes	—
356	C₂³×C₄	C₂³×C₇	1	8	yes	—
357	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₇	1	8	yes	complemented
359	#127	C₂³×C₇	1	32	yes	complemented
360	#127	C₂³×C₇	1	16	yes	complemented
361	#126	C₂³×C₇	1	64	yes	complemented
362	#125	C₂³×C₇	1	16	yes	complemented
363	#124	C₂³×C₇	1	32	yes	complemented
364	#123	C₂³×C₇	1	16	yes	complemented
365	#123	C₂³×C₇	1	64	yes	complemented
366	#123	C₂³×C₇	1	64	yes	complemented
367	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
368	#121	C₂³×C₇	1	32	yes	complemented
369	#121	C₂³×C₇	1	32	yes	complemented
370	#121	C₂³×C₇	1	32	yes	complemented
371	#121	C₂³×C₇	1	32	yes	complemented
372	#121	C₂³×C₇	1	16	yes	complemented
373	#121	C₂³×C₇	1	64	yes	complemented
374	#121	C₂³×C₇	1	32	yes	complemented
375	#121	C₂³×C₇	1	64	yes	complemented
376	#121	C₂³×C₇	1	64	yes	complemented
377	#120	C₂³×C₇	1	16	yes	complemented
378	#120	C₂³×C₇	1	32	yes	complemented
379	#120	C₂³×C₇	1	64	yes	complemented
380	#120	C₂³×C₇	1	32	yes	complemented
381	#120	C₂³×C₇	1	64	yes	complemented
382	C₄×D₄	C₂³×C₇	1	32	yes	complemented
383	C₄×D₄	C₂³×C₇	1	64	yes	complemented
384	C₄×D₄	C₂³×C₇	1	32	yes	complemented
385	#117	C₂³×C₇	1	8	yes	complemented
386	#117	C₂³×C₇	1	16	yes	complemented
387	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
393	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	complemented
402	C₂×C₄²	C₂³×C₇	1	2	yes	—
403	C₂×C₄²	C₂³×C₇	1	4	yes	—
404	C₂²×C₇	—	2	4	no	—
405	C₂²×C₇	—	2	4	no	—
406	C₂²×C₇	—	2	16	no	—
407	C₂²×C₇	—	2	2	no	—
408	C₂²×C₇	—	2	4	no	—
409	C₂²×C₇	—	2	16	no	—
410	C₂²×C₇	—	2	8	no	—
411	C₂²×C₇	—	2	16	no	—
412	C₂²×C₇	—	2	16	no	—
413	C₂²×C₇	—	2	4	no	—
414	C₂²×C₇	—	4	16	no	—
415	C₂²×C₇	—	4	4	no	—
416	C₂²×C₇	—	4	8	no	—
417	C₂²×C₇	—	4	32	no	—
418	C₂²×C₇	—	8	32	no	—
419	C₂²×C₇	—	8	32	no	—
420	C₂²×C₇	C₂×H(5,𝔽₂)	1	8	yes	—
421	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
422	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂²×C₇	C₂⁶	1	1	yes	characteristic
424	C₄×C₇	—	2	4	no	—
425	C₄×C₇	—	2	2	no	—
426	C₄×C₇	—	2	4	no	—
427	C₄×C₇	—	2	16	no	—
428	C₄×C₇	—	2	8	no	—
429	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
430	C₂⁴	—	2	8	no	—
431	C₂⁴	—	2	16	no	—
432	C₂⁴	—	4	2	no	—
433	C₂⁴	—	4	8	no	—
434	C₂⁴	—	4	8	no	—
435	C₂⁴	—	4	8	no	—
436	C₂⁴	—	4	16	no	—
437	C₂⁴	C₂⁴×C₇	1	2	yes	—
438	C₂⁴	C₂⁴×C₇	1	8	yes	—
439	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
440	C₂⁴	C₂⁴×C₇	1	4	yes	—
441	C₂⁴	C₂⁴×C₇	1	2	yes	—
442	C₂⁴	C₂⁴×C₇	1	16	yes	—
443	C₂⁴	C₂⁴×C₇	1	16	yes	—
444	#41	—	4	16	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
447	C₂×D₄	—	2	32	no	—
448	C₂×D₄	—	2	16	no	—
449	C₂×D₄	—	2	16	no	—
450	C₂×D₄	—	4	32	no	—
451	C₂×D₄	—	4	32	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	16	no	—
455	C₂×D₄	—	4	16	no	—
456	C₂×D₄	—	4	16	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	64	no	—
460	C₂×D₄	—	4	128	no	—
461	C₂×D₄	C₂⁴×C₇	1	16	yes	—
462	C₂×D₄	C₂⁴×C₇	1	32	yes	—
463	C₂×D₄	C₂⁴×C₇	1	16	yes	—
464	C₂×D₄	C₂⁴×C₇	1	4	yes	—
465	C₂×D₄	C₂⁴×C₇	1	8	yes	—
466	C₂×D₄	C₂⁴×C₇	1	16	yes	—
467	C₂×D₄	C₂⁴×C₇	1	32	yes	—
468	C₂×D₄	C₂⁴×C₇	1	32	yes	—
469	C₂×D₄	C₂⁴×C₇	1	16	yes	—
470	C₂×D₄	C₂⁴×C₇	1	32	yes	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	4	16	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	—	4	16	no	—
479	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
482	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
485	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
486	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
488	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
489	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
490	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
492	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
493	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
494	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
495	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
496	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
497	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
498	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
499	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
500	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
501	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
502	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
503	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
504	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
505	C₄²	C₂⁴×C₇	1	8	yes	—
506	C₄²	C₂⁴×C₇	1	16	yes	—
507	C₂×C₇	—	2	8	no	—
508	C₂×C₇	—	4	2	no	—
509	C₂×C₇	—	4	4	no	—
510	C₂×C₇	—	4	16	no	—
511	C₂×C₇	#3537	1	4	yes	direct product factor
512	C₂×C₇	C₂²×H(5,𝔽₂)	1	2	yes	—
513	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	16	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	16	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	32	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	16	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	16	no	—
529	C₂³	—	4	32	no	—
530	C₂³	—	4	16	no	—
531	C₂³	—	8	32	no	—
532	C₂³	—	8	32	no	—
533	C₂³	C₇×H(5,𝔽₂)	1	8	yes	—
534	C₂³	C₂⁵×C₇	1	4	yes	—
535	C₂³	C₂⁵×C₇	1	16	yes	—
536	C₂³	C₂⁵×C₇	1	2	yes	—
537	C₂³	C₂⁵×C₇	1	4	yes	—
538	C₂³	C₂⁵×C₇	1	1	yes	characteristic
539	Q₈	—	4	4	no	—
540	D₄	—	2	64	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	32	no	—
543	D₄	—	4	16	no	—
544	D₄	—	4	16	no	—
545	D₄	—	4	32	no	—
546	D₄	—	4	32	no	—
547	D₄	—	4	32	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	8	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	16	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	16	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	8	no	—
560	C₂×C₄	—	4	16	no	—
561	C₂×C₄	—	4	32	no	—
562	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
563	C₂×C₄	C₂⁵×C₇	1	4	yes	—
564	C₂×C₄	C₂⁵×C₇	1	8	yes	—
565	C₂×C₄	C₂⁵×C₇	1	16	yes	—
566	C₂×C₄	C₂⁵×C₇	1	2	yes	—
567	C₂×C₄	C₂⁵×C₇	1	4	yes	—
568	C₂×C₄	C₂⁵×C₇	1	2	yes	—
569	C₇	C₂×#3537	1	1	yes	characteristic, direct product factor, Sylow
570	C₂²	—	2	4	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	16	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	16	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	32	no	—
584	C₂²	—	8	32	no	—
585	C₂²	—	8	32	no	—
586	C₂²	C₂×C₇×H(5,𝔽₂)	1	8	yes	—
587	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
588	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
589	C₂²	C₂⁶×C₇	1	1	yes	characteristic
590	C₄	—	2	4	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	16	no	—
594	C₄	—	2	8	no	—
595	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
596	C₂	—	2	8	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	4	no	—
599	C₂	—	4	16	no	—
600	C₂	C₇×#3537	1	4	yes	direct product factor
601	C₂	C₂²×C₇×H(5,𝔽₂)	1	2	yes	—
602	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3537	C₂	direct (N × H)
2. C₂×C₇×#560	C₂	semidirect
3. C₂×C₇×#553	C₂	semidirect
4. C₂×C₇×D₄²	C₂	semidirect
5. C₂×C₇×D₄²	C₂	semidirect
6. C₂×C₇×#540	C₂	semidirect
7. C₂×C₇×#538	C₂	semidirect
8. C₂×C₇×#535	C₂	semidirect
9. C₂×C₇×#534	C₂	semidirect
10. C₂×C₇×#525	C₂	semidirect
11. C₂²×C₇×#121	C₂	semidirect
12. C₂²×C₇×#41	C₂²	semidirect
13. C₂³×C₇×D₄	C₂²	semidirect
14. C₂³×C₇×D₄	C₂²	semidirect
15. C₂³×C₇×D₄	C₂²	semidirect
16. C₂³×C₇×D₄	C₂²	semidirect
17. C₂⁴×C₄×C₇	C₂²	semidirect
18. C₇×#560	C₂²	semidirect
19. C₇×#553	C₂²	semidirect
20. C₇×D₄²	C₂²	semidirect
21. C₇×D₄²	C₂²	semidirect
22. C₇×#540	C₂²	semidirect
23. C₇×#538	C₂²	semidirect
24. C₇×#535	C₂²	semidirect
25. C₇×#534	C₂²	semidirect
26. C₂×C₇×#127	C₂²	semidirect
27. C₂×C₇×#127	C₂²	semidirect
28. C₂×C₇×#126	C₂²	semidirect
29. C₂×C₇×#125	C₂²	semidirect
30. C₂×C₇×#124	C₂²	semidirect
31. C₇×#525	C₂²	semidirect
32. C₂×C₇×#123	C₂²	semidirect
33. C₂×C₇×#123	C₂²	semidirect
34. C₂×C₇×#123	C₂²	semidirect
35. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₇×#121	C₂²	semidirect
37. C₂×C₇×#121	C₂²	semidirect
38. C₂×C₇×#121	C₂²	semidirect
39. C₂×C₇×#121	C₂²	semidirect
40. C₂×C₇×#121	C₂²	semidirect
41. C₂×C₇×#121	C₂²	semidirect
42. C₂×C₇×#121	C₂²	semidirect
43. C₂×C₇×#121	C₂²	semidirect
44. C₂×C₇×#121	C₂²	semidirect
45. C₂×C₇×#121	C₂²	semidirect
46. C₂×C₇×#120	C₂²	semidirect
47. C₂×C₇×#120	C₂²	semidirect
48. C₂×C₇×#120	C₂²	semidirect
49. C₂×C₇×#120	C₂²	semidirect
50. C₂×C₇×#120	C₂²	semidirect
51. C₂×C₄×C₇×D₄	C₂²	semidirect
52. C₂×C₄×C₇×D₄	C₂²	semidirect
53. C₂×C₄×C₇×D₄	C₂²	semidirect
54. C₂×C₇×#117	C₂²	semidirect
55. C₂×C₇×#117	C₂²	semidirect
56. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
57. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
58. C₂×#3537	C₇	direct (N × H)
63. C₂×C₇×#41	C₂³	semidirect
79. C₂²×C₇×D₄	C₂³	semidirect
80. C₂²×C₇×D₄	C₂³	semidirect
81. C₂²×C₇×D₄	C₂³	semidirect
82. C₂²×C₇×D₄	C₂³	semidirect
91. C₂³×C₄×C₇	C₂³	semidirect
92. C₇×#127	C₂³	semidirect
93. C₇×#127	C₂³	semidirect
94. C₇×#126	C₂³	semidirect
95. C₇×#125	C₂³	semidirect
96. C₇×#124	C₂³	semidirect
97. C₇×#123	C₂³	semidirect
98. C₇×#123	C₂³	semidirect
99. C₇×#123	C₂³	semidirect
100. C₇×C₂²⋊Q₈	C₂³	semidirect
101. C₇×#121	C₂³	semidirect
102. C₇×#121	C₂³	semidirect
103. C₇×#121	C₂³	semidirect
104. C₇×#121	C₂³	semidirect
105. C₇×#121	C₂³	semidirect
106. C₇×#121	C₂³	semidirect
107. C₇×#121	C₂³	semidirect
108. C₇×#121	C₂³	semidirect
109. C₇×#121	C₂³	semidirect
110. C₇×#120	C₂³	semidirect
111. C₇×#120	C₂³	semidirect
112. C₇×#120	C₂³	semidirect
113. C₇×#120	C₂³	semidirect
114. C₇×#120	C₂³	semidirect
115. C₄×C₇×D₄	C₂³	semidirect
116. C₄×C₇×D₄	C₂³	semidirect
117. C₄×C₇×D₄	C₂³	semidirect
118. C₇×#117	C₂³	semidirect
119. C₇×#117	C₂³	semidirect
125. C₂×C₇×C₄⋊C₄	C₂³	semidirect
134. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
137. #3537	C₂×C₇	direct (N × H)
138. C₂×#560	C₂×C₇	semidirect
139. C₂×#553	C₂×C₇	semidirect
140. C₂×D₄²	C₂×C₇	semidirect
141. C₂×D₄²	C₂×C₇	semidirect
142. C₂×#540	C₂×C₇	semidirect
143. C₂×#538	C₂×C₇	semidirect
144. C₂×#535	C₂×C₇	semidirect
145. C₂×#534	C₂×C₇	semidirect
146. C₂×#525	C₂×C₇	semidirect
147. C₂²×#121	C₂×C₇	semidirect
225. C₂²×#41	C₂²×C₇	semidirect
226. C₂³×D₄	C₂²×C₇	semidirect
227. C₂³×D₄	C₂²×C₇	semidirect
228. C₂³×D₄	C₂²×C₇	semidirect
229. C₂³×D₄	C₂²×C₇	semidirect
230. C₂⁴×C₄	C₂²×C₇	semidirect
231. #560	C₂²×C₇	semidirect
232. #553	C₂²×C₇	semidirect
233. D₄²	C₂²×C₇	semidirect
234. D₄²	C₂²×C₇	semidirect
235. #540	C₂²×C₇	semidirect
236. #538	C₂²×C₇	semidirect
237. #535	C₂²×C₇	semidirect
238. #534	C₂²×C₇	semidirect
239. C₂×#127	C₂²×C₇	semidirect
240. C₂×#127	C₂²×C₇	semidirect
241. C₂×#126	C₂²×C₇	semidirect
242. C₂×#125	C₂²×C₇	semidirect
243. C₂×#124	C₂²×C₇	semidirect
244. #525	C₂²×C₇	semidirect
245. C₂×#123	C₂²×C₇	semidirect
246. C₂×#123	C₂²×C₇	semidirect
247. C₂×#123	C₂²×C₇	semidirect
248. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
249. C₂×#121	C₂²×C₇	semidirect
250. C₂×#121	C₂²×C₇	semidirect
251. C₂×#121	C₂²×C₇	semidirect
252. C₂×#121	C₂²×C₇	semidirect
253. C₂×#121	C₂²×C₇	semidirect
254. C₂×#121	C₂²×C₇	semidirect
255. C₂×#121	C₂²×C₇	semidirect
256. C₂×#121	C₂²×C₇	semidirect
257. C₂×#121	C₂²×C₇	semidirect
258. C₂×#121	C₂²×C₇	semidirect
259. C₂×#120	C₂²×C₇	semidirect
260. C₂×#120	C₂²×C₇	semidirect
261. C₂×#120	C₂²×C₇	semidirect
262. C₂×#120	C₂²×C₇	semidirect
263. C₂×#120	C₂²×C₇	semidirect
264. C₂×C₄×D₄	C₂²×C₇	semidirect
265. C₂×C₄×D₄	C₂²×C₇	semidirect
266. C₂×C₄×D₄	C₂²×C₇	semidirect
267. C₂×#117	C₂²×C₇	semidirect
268. C₂×#117	C₂²×C₇	semidirect
269. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
270. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
330. C₂×#41	C₂³×C₇	semidirect
346. C₂²×D₄	C₂³×C₇	semidirect
347. C₂²×D₄	C₂³×C₇	semidirect
348. C₂²×D₄	C₂³×C₇	semidirect
349. C₂²×D₄	C₂³×C₇	semidirect
358. C₂³×C₄	C₂³×C₇	semidirect
359. #127	C₂³×C₇	semidirect
360. #127	C₂³×C₇	semidirect
361. #126	C₂³×C₇	semidirect
362. #125	C₂³×C₇	semidirect
363. #124	C₂³×C₇	semidirect
364. #123	C₂³×C₇	semidirect
365. #123	C₂³×C₇	semidirect
366. #123	C₂³×C₇	semidirect
367. C₂²⋊Q₈	C₂³×C₇	semidirect
368. #121	C₂³×C₇	semidirect
369. #121	C₂³×C₇	semidirect
370. #121	C₂³×C₇	semidirect
371. #121	C₂³×C₇	semidirect
372. #121	C₂³×C₇	semidirect
373. #121	C₂³×C₇	semidirect
374. #121	C₂³×C₇	semidirect
375. #121	C₂³×C₇	semidirect
376. #121	C₂³×C₇	semidirect
377. #120	C₂³×C₇	semidirect
378. #120	C₂³×C₇	semidirect
379. #120	C₂³×C₇	semidirect
380. #120	C₂³×C₇	semidirect
381. #120	C₂³×C₇	semidirect
382. C₄×D₄	C₂³×C₇	semidirect
383. C₄×D₄	C₂³×C₇	semidirect
384. C₄×D₄	C₂³×C₇	semidirect
385. #117	C₂³×C₇	semidirect
386. #117	C₂³×C₇	semidirect
392. C₂×C₄⋊C₄	C₂³×C₇	semidirect
401. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
511. C₂×C₇	#3537	direct (N × H)
569. C₇	C₂×#3537	direct (N × H)
600. C₂	C₇×#3537	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3537	2
C₂×C₇×#560	2
C₂×C₇×#553	2
C₂×C₇×D₄²	2
C₂×C₇×#540	2
C₂×C₇×#538	2
C₂×C₇×#535	2
C₂×C₇×#534	2
C₂×C₇×#525	2
C₂²×C₇×#121	2
C₂×#3537	7

Subgroups — C2×C7×#3537 #13239940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3537 #13239940